In this article, we show that a class of high frequencies of the threedimensional linearized elasticity system in a thin rod and their associated eigenfunctions converge in a precise sense, as the area of the cross section of the rod goes to zero. The limit model is a coupled one-dimensional problem giving the classical equations for torsion and stretching modes in rods.

Contents Introduction-a shape problem in planar elasticity 1 1. Modeling, stationary solutions and shape calculus 3 1.1. The optimization problems 3 1.2. Shape calculus and necessary condition 4 1.3. Stationary shapes 6 2. Approximation for the shapes and optimization algorithms 8 2.1. Finite dimensional representation of boundaries 8 2.2. Relaxation of the constraints 9 2.3. Descent methods of...

A general Nitsche method, which encompasses symmetric and non-symmetric variants, is proposed for frictionless unilateral contact problems in elasticity. The optimal convergence of the method is established both for two and three-dimensional problems and Lagrange affine and quadratic finite element methods. Two and three-dimensional numerical experiments illustrate the theory.

In this paper, an analytic solution is presented using differential transform method (DTM) for a class of wave equation. The emphasis is on the nonlinear two-dimensional wave equation. The procedures introduced in this paper are in recursive forms which can be used to obtain the closed form of the solutions, if they are required. The method is tested on various examples, and the results reveal ...

The singularities that we consider are the characteristic non-smooth solutions of the equations of linear elasticity in piecewise homogeneous media near two dimensional corners or three dimensional edges. We describe here a method to compute their singularity exponents and the associated angular singular functions. We present the implementation of this method in a program whose input data are g...

We analyze the welfare impacts of price discrimination in a two-dimensional spatial differentiation model. Consumer information of varying qualities is available on one dimension which allows firms to price discriminate, and better information leads to more refined price discrimination. We find that as information quality improves, firms’ profits monotonically increase while consumer surplus an...

Dimensional analysis, for multi-criteria decision making, is a mathematical method that includes diverse heterogeneous criteria into a single dimensionless index. Dimensional Analysis, in its current definition, presents the drawback to manipulate fuzzy information commonly presented in a multi-criteria decision making problem. To overcome such limitation, we propose two dimensional analysis ba...

in this present study, volume of fluid method in openfoam open source cfd package will be extended to consider phase change phenomena with modified model due to condensation and boiling processes. this model is suitable for the case in which both unsaturated phase and saturated phase are present and for beginning boiling and condensation process needn't initial interface. both phases (liqu...

Natural convection between vertical parallel plates occurs frequently in applications such as solar collectors and cooling of electronic instruments. The problem is a two dimensional developing buoyant flow. In this work, the two dimensional conservation equations are solved numerically for constant wall temperature and constant wall heat flux. The results for the local Nusselt number at the du...